The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A299019 Expansion of Product_{k>=1} (1 - x^k)^(k+1). 1
 1, -2, -2, 2, 3, 6, -1, -2, -10, -14, -7, -2, 11, 26, 43, 30, 28, -6, -40, -92, -128, -132, -115, -48, 54, 200, 339, 484, 499, 476, 274, -32, -501, -998, -1539, -1924, -2042, -1838, -1139, 12, 1664, 3540, 5588, 7258, 8392, 8230, 6812, 3480, -1472, -8150, -15737, -23670, -30478 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Convolution of A010815 and A073592. Convolution inverse of A005380. LINKS FORMULA G.f.: exp(-Sum_{k>=1} (sigma_1(k) + sigma_2(k))*x^k/k). MATHEMATICA nmax = 52; CoefficientList[Series[Product[(1 - x^k)^(k + 1), {k, 1, nmax}], {x, 0, nmax}], x] nmax = 52; CoefficientList[Series[Exp[-Sum[(DivisorSigma[1, k] + DivisorSigma[2, k]) x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] a[n_] := a[n] = If[n == 0, 1, -Sum[Sum[d (d + 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 52}] CROSSREFS Cf. A005380, A010815, A073592, A092346. Sequence in context: A121256 A022867 A268595 * A070610 A156820 A104346 Adjacent sequences:  A299016 A299017 A299018 * A299020 A299021 A299022 KEYWORD sign AUTHOR Ilya Gutkovskiy, Aug 11 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 13 11:33 EDT 2021. Contains 344990 sequences. (Running on oeis4.)